How do you simplify (square root of 6/square root of 7) * (square root of 14/square root of 3)?

2 Answers
Hasna K.
Apr 2, 2018

Write the roots as their factors..

Explanation:

#(sqrt6/sqrt7)*(sqrt14/sqrt3)#
Because we are multiplying the two fractions, we know that we can simplify by cancelling right?
Write each of the fractions, if possible, in their factors . For example : #sqrt6=sqrt2*sqrt3#

You should get this : #((sqrt2*sqrt3)/sqrt7)*((sqrt7*sqrt2)/sqrt3)#
Cancel out any factor that is both in the numerator and the denominator.
You should be left with root 2 times root 2, which is 2 :)

Barney V.
Apr 2, 2018

#2#

Explanation:

#sqrt6/sqrt7*sqrt14/sqrt3#

#:.=sqrt84/sqrt21#

#:.=sqrt(2*2*3*7)/sqrt21#

#:.sqrt2*sqrt2=2#

#:.=(2sqrt(3*7))/sqrt21#

#:.=(2cancelsqrt21^1)/cancelsqrt21^1#

#:.=2#

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